# Revealing the Majority Winner

Bart Ingles bartman at netgate.net
Fri Nov 13 23:20:34 PST 1998

```>  Bart Ingles wrote:
> .<SNIP>
> > As I mentioned in my reply to Blake, when the actual level of support is
> > unknown, I tend to assume a lower value rather than the 'more-or-less
> > equidistant between top and bottom' value that people seem to infer from
> > the rankings.
> >
> > In other words, the middle candidate could be only marginally higher
> > than the bottom candidate, in which case it seems safer to give more
> > weight to the top rank.

David Marsay wrote:

> Interesting. I tend to take the opposite view.

Bart writes:

I wonder if this is an underlying view that differentiates IRO and
Condorcet supporters?

scale, rather than just rank them.  Higher score means more highly
favored.  The same election could come out a couple of different ways (I
hope you are using a fixed font):

Rating: 100    80    60    40    20    0
----------------------------------------
45       A  B                          C
15       B                          C  A
40       C  B                          A

-or-

45       A                          B  C
15       B  C                          A
40       C                          B  A

Neither IRO nor Condorcet can distinguish between the two cases.

I think it would be a mistake to pretend these voter preferences don't
exist, just because relative ranking doesn't measure them.  After a
(ranked) Condorcet election where voters' real preferences are like the
second example, imagine the backlash when some enterprising pollster
reports that when asked to rate the candidates on a 100-point scale,
voters gave the winner a median rating of 10, while one of the losers
had a median score of 90!  (Highest median score -- now there's a
method.  :-)

On the other hand, top example is no ringing endorsement of IRO.  Winner
(C) had a median score of 10, while loser (B) had a median of 90.
Surprisingly (to me at least), Approval is the only widely discussed
method on this list that would have had a chance of handling both cases
equally well, at least without being heavily "repaired" by strategy.  I
would have thought that Approval depended more heavily on strategy than
other methods, I guess not when you are concerned about more than
ranking.  Then again, these examples probably couldn't be more